Two non-conducting spheres of radii and and carrying uniform volume charge densities and , respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region [2013]

Question

Two non-conducting spheres of radii $R_{1}$ and $R_{2}$ and carrying uniform volume charge densities $+ ρ$ and $- ρ$ , respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region [2013]

Smart Achievers · Accepted Answer

(3, 4)

Electrostatic field at P is

${\vec{E}}_{P} = {\vec{E}}_{1} + {\vec{E}}_{2} = \frac{ρ}{3 ε_{0}} \vec{C_{1} P} + \frac{(- ρ)}{3 ε_{0}} \vec{C_{2} P}$

$= \frac{ρ}{3 ε_{0}} (\vec{C_{1} P} - \vec{C_{2} P})$ $= \frac{ρ}{3 ε_{0}} (\vec{C_{1} P} + \vec{P C_{2}})$ $= \frac{ρ}{3 ε_{0}} (\vec{C_{1} C_{2}})$

Solution

Q.
Two non-conducting spheres of radii $R_{1}$ and $R_{2}$ and carrying uniform volume charge densities $+ ρ$ and $- ρ$ , respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region [2013]

1 The electrostatic field is zero

2 The electrostatic potential is constant

3 The electrostatic field is constant in magnitude

4 The electrostatic field has the same direction

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